Important to remember that the phrase should really be “correlation does not *necessarily* imply causation.” Correlation *can* be evidence of a causative link. This happens when the correlation is seen consistently, potential confounding factors are controlled for, there’s a mechanistic reason to believe the link is causal, and there’s other experimental evidence that implies a link.
Smoking causing cancer is a good example. All we really have for this in humans in correlational data, because it’s unethical to perform direct experiments on humans. But the correlational data is very high quality, there’s a biological reason to think the causal link exists, and animal experiments show a direct relationship.
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